The conventional electroerosion machining technique commonly calls for a tool electrode in the form of a shaped block or metal sheet, a wire, a simple rod or the like, whose contour is reproduced directly or indirectly in a workpiece to constitute a desired cavity therein. The tool electrode must, therefore, be shaped and sized precisely to correspond to the desired cavity shape and size. In modern electroerosion machining systems, the tool electrode is displaced relative to the workpiece three-dimensionally or with three degrees of freedom along a prescribed path which, in conjunction with the shape and size of the tool electrode, determines the ultimate shape and size of a cavity desired in the workpiece. The tool electrode may, however, wear erosively during a given course of machining operation with an electroerosion process. The electrode wear may be reduced substantially to nil with a certain combination of machining parameters but may become significant with a diverse range of combinations of machining parameters which are preferred or desirable. The electrode wear then reaches a stage which requires a repeated electrode replacement or instantaneous corrections of the position of the tool electrode in a predetermined feed displacement path. These measures are generally troublesome, involve relatively sophisticated and expensive means and procedures and are therefore undesirable.